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Simple polynomial regression for single feature in Python
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is an example of simple polynomial regression for single feature.\n",
"As a dataset I'm using calibration data of high pressure densitometer.\n",
"My goal was to make an equation, that's can decribe relationship between temperature and period of oscillation of densitometer's U-tube."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First import all libralies we will need."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import pandas as pd\n",
"from pylab import show, plot,xlabel, ylabel, title, subplot, draw\n",
"import numpy as np\n",
"from sklearn.metrics import mean_squared_error\n",
"from math import sqrt\n",
"\n",
"\n",
"#Then import our dataset\n",
"\n",
"df = pd.read_csv('Argon periods3000.csv')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Before bilding any regression models, lets first look at our data and check thats everything is fine"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>temp</th>\n",
" <th>period</th>\n",
" <th>pressure</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>21.3</td>\n",
" <td>2616.756389</td>\n",
" <td>3000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>23.8</td>\n",
" <td>2617.280000</td>\n",
" <td>3000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>24.3</td>\n",
" <td>2617.410000</td>\n",
" <td>3000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>25.0</td>\n",
" <td>2617.524000</td>\n",
" <td>3000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>27.0</td>\n",
" <td>2617.950000</td>\n",
" <td>3000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" temp period pressure\n",
"0 21.3 2616.756389 3000\n",
"1 23.8 2617.280000 3000\n",
"2 24.3 2617.410000 3000\n",
"3 25.0 2617.524000 3000\n",
"4 27.0 2617.950000 3000"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So my datasets have 3 columns: Temperature, Period of oscillation my densitometer and Pressure "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>temp</th>\n",
" <th>period</th>\n",
" <th>pressure</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>count</th>\n",
" <td>31.000000</td>\n",
" <td>31.000000</td>\n",
" <td>31</td>\n",
" </tr>\n",
" <tr>\n",
" <th>mean</th>\n",
" <td>40.154839</td>\n",
" <td>2621.031464</td>\n",
" <td>3000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>std</th>\n",
" <td>12.302895</td>\n",
" <td>2.934271</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>min</th>\n",
" <td>21.300000</td>\n",
" <td>2616.756389</td>\n",
" <td>3000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25%</th>\n",
" <td>29.200000</td>\n",
" <td>2618.430000</td>\n",
" <td>3000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>50%</th>\n",
" <td>39.400000</td>\n",
" <td>2620.699000</td>\n",
" <td>3000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>75%</th>\n",
" <td>46.600000</td>\n",
" <td>2622.455000</td>\n",
" <td>3000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>max</th>\n",
" <td>62.700000</td>\n",
" <td>2626.612000</td>\n",
" <td>3000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" temp period pressure\n",
"count 31.000000 31.000000 31\n",
"mean 40.154839 2621.031464 3000\n",
"std 12.302895 2.934271 0\n",
"min 21.300000 2616.756389 3000\n",
"25% 29.200000 2618.430000 3000\n",
"50% 39.400000 2620.699000 3000\n",
"75% 46.600000 2622.455000 3000\n",
"max 62.700000 2626.612000 3000"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.describe()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With describe function I look in dataset more closely to check if my data have same amount of rows, and also checking for errors and anomalies. So everything looks fine."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Then I making plot to visualize my Period-temperatute relationship"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"x= df['temp']\n",
"y= df['period']\n",
"plot(x,y,'co')\n",
"xlabel('Temperature')\n",
"ylabel('Period')\n",
"title('Period-temperature relationship')\n",
"show() "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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/+PymIvby8lJWVpbLuj+65rx7k9fmlStXuhxwfrU25/ezO3PmjBo1aqQDBw6oSZMm6tOn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\nbTYk4IyO3YEAAAAASUVORK5CYII=\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#code below is to display image in IPython\n",
"from IPython.display import Image\n",
"Image(filename='figure_1.1.png')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So it's look pretty linear.\n",
"Let's make Linear regression and check how it's fits "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"regression1 = np.polyfit(x, y, 1)\n",
"#y basicaly is calculated Period values from our model \n",
"y1 = regression1[0]*x+regression1[1]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's plot our experimantal and our calculated values"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"plot(x,y,'co')\n",
"plot(x,y1)\n",
"xlabel('Temperature')\n",
"ylabel('Period')\n",
"title('Period-temperature relationship')"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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Lr7wSlFRvvRUUU8OHw623QsWKYaeTJEkllWWV\nJEmSJElSMbdvH0yeDMnJkJERbPH33HPQqROU9qdDkiQpZP7viCRJkiRJUjH19dfw2GPB1zffQMeO\n8NRT0KIFOJZZkiQVFpZVkiRJkiRJxczKlcEqqmefDVZO9ekDAwZA3bphJ5MkSTqcZZUkSZIkSVIx\nEI3Cm28G86hefRVOPx2GDYN+/eCUU8JOJ0mSdGSWVZIkSZIkSUXYd9/BtGlBSfWvf0HjxsF8qptu\ngpNOCjudJEnST7OskiRJkiRJKoK++QbGjoUxY2DLFmjXDlJT4cornUclSZKKFssqSZIkSZKkIuSz\nzyAlBSZMCLb+69kTBg6E884LO5kkSdLxsaySJEmSJEkq5KJReO+9YKu/uXMhLg7+8Ae47bbgz5Ik\nSUWZZZUkSZIkSVIhlZUFzz8flFRLlkDDhvDUU/Cb30DZsmGnkyRJyh+WVZIkSZIkSYXMjh3w5JMw\nahR8+SX8+tfw6qvQpo3zqCRJUvFjWSVJkiRJklRIrFsHqanw9NPw3XeQmAh33w2NGoWdTJIkqeBY\nVkmSJEmSJIVs4cJgq79Zs6ByZRg4EO64A047LexkkiRJBc+ySpIkSZIkKQQ5OTB7dlBSLVwIZ58N\nY8ZAz55QvnzY6SRJkk4cyypJkiRJkqQTaPduGD8+2O5v3Tq44gqYMwfatYOYmLDTSZIknXiWVZIk\nSZIkSSfAl1/CqFEwbhxkZkLXrvD889C0adjJJEmSwmVZJUmSJEmSVICWLoURI2DGDIiNhX79oH9/\nqFkz7GSSJEmFg2WVJEmSJElSPsvNhXnzgnlU774LdeoEhVXv3lChQtjpJEmSChfLKkmSJEmSpHyy\ndy9MnAjJybB6NTRvDi+8AB06QKlSYaeTJEkqnCyrJEmSJEmSfqYtW2DMGHj8cdixAzp1Ckqr5s3D\nTiZJklT4WVZJkiRJkiQdp3/9K9jqb+pUOOkkuPVWGDAg2PZPkiRJR8eySpIkSZIk6RhEo/D668EM\nqjfegDPPhKQk6NsXKlcOO50kSVLRY1klSZIkSZJ0FPbvhylTgnlUK1dCkybB5y5doEyZsNNJkiQV\nXZZVkiRJkiRJP2LbtmAW1d//Hvy5ffvgz5dfDpFI2OkkSZKKPssqSZIkSZKkPGRkBKuoJk0KSqle\nvWDgQDjnnLCTSZIkFS+WVZIkSZIkSf8RjcI77wTzqF56CWrUgKFD4bbb4NRTw04nSZJUPFlWSZIk\nSZKkEu/AAZgxA0aOhI8/hkaN4JlnoHt3+MUvwk4nSZJUvFlWSZIkSZKkEuvf/4Zx42DUKNi0Ca69\nFl5/Ha6+2nlUkiRJJ4pllSRJkiRJKnHWroXUVBg/HrKy4OabYdAgaNgw7GSSJEklj2WVJEmSJEkq\nEaJR+OCDYB7Viy8GM6juuQfuuAOqVw87nSRJUsllWSVJkiRJkoq17GyYNSsoqRYtgnPPhbFjg9VU\n5cqFnU6SJEmWVZIkSZIkqVjatQuefjrY7m/9emjVCubNg7ZtISYm7HSSJEn6nmWVJEmSJEkqVjZs\ngFGj4MknYe9e6N49mEd1wQVhJ5MkSVJeLKskSZIkSVKxsHgxjBwJzz8PFSoEs6juvBPOOCPsZJIk\nSfoxllWSJEmSJKnIysmBuXODeVTvvw+//CWkpECvXnDyyWGnkyRJ0tGwrJIkSZIkSUXOnj0wYUJQ\nTK1ZA5deCrNmwQ03QKlSYaeTJEnSsbCskiRJkiRJRcamTTBmDIwdCzt3QufOMGUKNGsWdjJJkiQd\nL8sqSZIkSZJU6H3ySTCPato0KFsW+vaF/v2hdu2wk0mSJOnnsqySJEmSJEmFUm4uvPpqUFLNnw9n\nnQUPPwy33gqVKoWdTpIkSfnFskqSJEmSJBUq+/bBs89CcjKkp8NFF8H06XDjjVDan2RIkiQVO/4v\nniRJkiRJKhS2boXHHgu+tm+HDh1g3Dho2RIikbDTSZIkqaBYVkmSJEmSpFCtWhWsopo8GUqVgj59\nYMAAqFcv7GSSJEk6ESyrJEmSJEnSCReNBnOoRo6EV16B00+HP/8Z+vWDKlXCTidJkqQTybJKkiRJ\nkiSdMN99F8yfGjkSli+HX/0KJk2Crl3hpJPCTidJkqQwWFZJkiRJkqQC9+23MHYsjBkDmzfDddcF\nW/+1auU8KkmSpJLOskqSJEmSJBWY1ashJQUmTICcHLjlFhg0COrXDzuZJEmSCgvLKkmSJEmSlK+i\nUViwINjqb84cqFoVBg+G22+HatXCTidJkqTCxrJKkiRJkiTli6wseOGFoKT65z+D1VPjxkGPHlC2\nbNjpJEmSVFhZVkmSJEmSpJ9l50548kkYNQo2boSrr4aXX4ZrroGYmLDTSZIkqbCzrJIkSZIkScfl\niy8gNRWeegq++w5+8xu4+244//ywk0mSJKkosaySJEmSJEnH5MMPg63+Zs6ESpXgrrvgzjvhtNPC\nTiZJkqSiyLJKkiRJkiT9pJwcePHFoKT64AOoVw9Gj4aePSE2Nux0kiRJKsosqyRJkiRJ0hFlZsL4\n8ZCSAuvWweWXB6VV+/bOo5IkSVL+sKySJEmSJEmH+fLLYOXUE08EhdVNN8GMGXDhhWEnkyRJUnFj\nWSVJkiRJkg5aujTY6u+556B8eejXL5hJVbNm2MkkSZJUXFlWSZIkSZJUwn399TYS+85m4YJm7N3R\nmDJlt3BB8w94buLl1KlTNex4kiRJKubcXVqSJEmSpBJq71549NFd1Ky9l/lz+7H3tDrwp5VkzUln\ncbct/DrxBrZt2xZ2TEmSJBVzllWSJEmSJJUwW7bAH/8IZ50FgwefTNZ52TB6KTz2MVy5DcpEoEED\n1iYmMjgpKey4kiRJKuYsqyRJkiRJKiFWrIA+faBWLUhOhsREqHvJLTByA8TvOvyG+vVZtGLFiQ8q\nSZKkEsWySpIkSZKkYiwahddfh2uugUaNgj//5S+wcSOkpkJM+S0QieR9c0wM2Uc6J0mSJOWT0mEH\nkCRJkiRJ+e+772DqVBg5MlhRdcEF8Oyz0KULnHTSD9eVjkaDRiuvUio3NzgvSZIkFSBXVkmSJEmS\nVIxs3w5JScFWf336QJ068PbbsGRJsO3f/y2qAJrFx0N6et4PS08PzkuSJEkFyJVVkiRJkiQVA59+\nGsyhmjgx+NyzJwwaBOee++P3DR86lAUJCaxNTIT69SEmBnJzIT2dulOmMDwtreDDS5IkqUSzrJIk\nSZIkqYiKRuHdd2HECJg3D6pXhyFD4LbboGrVo3tGXFwcC9PSGJyUxKJZs8iORCgdjdIsPp7haWnE\nxcUV7EtIkiSpxLOskiRJkiSpiMnKghkzgnlUS5dCfDyMHw/du0PZssf+vLi4OJ5JTc3/oJIkSdJR\nsKySJEmSJKmI+Pe/4cknYdQo+OoraNMGXnsNfv1riETCTidJkiQdH8sqSZIkSZIKuc8/h9RUePrp\nYFVVYiLcfXewokqSJEkq6iyrJEmSJEkqpD74INjqb/ZsOOUUGDQIfv97qFEj7GSSJElS/rGskiRJ\nkiSpEMnODsqpkSPhww/hnHPgscfg5puhfPmw00mSJEn5z7JKkiRJkqRCYPfuYJu/1FT44gu44gqY\nMwfatYOYmLDTSZIkSQXHskqSJEmSpBBt3AijRsG4cbB3L3TtCjNnQpMmYSeTJEmSTgzLKkmSJEmS\nQrBkCYwYATNmwMknw223Qf/+cOaZYSeTJEmSTizLKkmSJEmSTpDcXJg3Lyip3nsP6tQJZlP16RMU\nVtu2baP3gCQWrVhBdiRC6WiUZvHxDB86lLi4uLDjS5IkSQXCskqSJEmSpAK2dy9MmAApKbB6NbRo\nEWz1l5AApUoF12zdupUWHTqwtkcP6NABIhHIzWVVRgYLEhJYmJZmYSVJkqRiyRGtkiRJkiQVkM2b\nYehQqFkz2OKvcWNYuBD+8Q/o1OmHogrg/gcfDIqqBg2CogogJgYaNGBtYiKDk5LCeQlJkiSpgFlW\nSZIkSZKUz5Yvh169oFYtSE2FW26BtWuD+VSXXJL3PYtWrID69fM+Wb9+cF6SJEkqhtwGUJIkSZKk\nfBCNwmuvBTOo3ngjWE3117/Cb38LlSr99P3ZkcgPK6r+W0xMcF6SJEkqhiyrJEmSJEn6GfbvhylT\ngpJq1Spo2hSmToXOnaFMmaN/TuloNGi88iqlcnOD85IkSVIx5DaAkiRJkiQdh23bYNgwOOss6NsX\nzjrrO669cRR7K7bmz09fTeNrW9N7wAC2bdt2VM9rFh8P6el5n0xPD85LkiRJxZArqyRJkiRJOgbp\n6ZCcDJMmQUwM9O4NPXp8w833tGdt+x5Qf2iwOio3l1UZGSxISGBhWhpxcXE/+tzhQ4eyICGBtYmJ\nweyqmBjIzYX0dOpOmcLwtLQT9IaSJEnSieXKKkmSJEmSfkI0Cm+9Be3aQYMGMHcu/M//wMcfb2dv\n6QG07d0yKJkaNPhhG7+YGGjQgLWJiQxOSvrJ7xEXF8fCtDR6ffYZDR58kHOSkmjw4IP0+uyzoyq7\nJEmSpKLKlVU6LhMnTiRyHMN9b7nllgJII0mSJEkF48ABeO65YB7VsmVw/vkwYQJ06wY7d26lRYcO\nrO3RAz76KCiq8lK/PotmzTqq7xcXF8czqan59wKSJElSEWBZpePSu3fv47rPskqSJElSUfDttzBu\nHIweDZs2Qdu28Mgj0Lr1Dwun7n/wwaCoatAASpX64cR/i4kh+zh+2U+SJEkqKSyrdFw+//zzQz7v\n2LGDnj17UrlyZfr3788555wDwKeffsro0aPZtWsXEydODCOqJEmSJB21NWsgNRXGj4ecHLj5Zhg4\nEBo2PPzaRStWQIcOwYecnGCvwLxKqdxcSkejBRtckiRJKsIsq3RcateufcjnXr16ERcXx+uvv05M\nzA+j0M4//3w6depEmzZtSE5OZsKECSc2qCRJkiT9hGgU/vGPYKu/F1+EU0+F++6D22+H6tWPfF92\nJPJDOVW7NqSn570VYHo6zeLjCyS7JEmSVBzE/PQl0k9LS0ujU6dOhxRV3ytVqhSdOnUiLS0thGSS\nJEmSlLfs7GAe1SWXwGWXBV3TE0/Ahg3w5z//eFEFBKulvl8x1a0bPPUUrFwJubnBsdxcWLmSulOm\nMHzo0AJ9F0mSJKkoc2WV8kVubi7p6elHPJ+enk7UbS8kSZIkFQK7dgW9UmpqUEy1bg0vvQTXXgt5\n/P7dETWLj2fV96upKleG//kfmD4dJk+G7Gwq7dtHx6uvZnhaGnFxcQX3QpIkSVIRZ1mlfNGxY0ce\nf/xxateuze2330758uUB2LNnD48//jhjx44lMTEx5JSSJEmSSrKlS7/hlt8uJ315M3JzT6JS9bdp\n330ZT6f2Pq4yafjQoSxISGBtYiLUrx8UVv36QXo6dadMYeErr1hSSZIkSUfBskr5IiUlhXXr1nHf\nfffxwAMPcNpppxGNRtm8eTPZ2dm0bNmSlJSUsGNKkiRJKoEWLYKHHtpPWlolKN8cun4NHb9iZ5XS\nzM04meYJCSw8jtVPcXFxLExLY3BSEotmzSI7EqF0NEqz+HhXU0mSJEnHwLJK+aJy5cq88847zJkz\nh5dffpn169cDcO2119KuXTvat29P5PvBw5IkSZJUwHJyYM4cGDkS3n8fKlTaDTelQy+g3H9mShED\nDRqwNjGRwUlJPJOaeszfJy4u7rjukyRJkvQDyyrlm0gkQkJCAgkJCWFHkSRJklRCZWbChAmQkgJr\n18Jll8Hs2fDAqN+QftsDkNcv0dWvz6JZs054VkmSJEkByyrlq8zMTN57772DK6tq1arFFVdcQWxs\nbMjJJEmSJBVnmzbB6NHwxBOwaxd06QJTp0KzZsH5+8dE8y6qAGJiyHYnCEmSJCk0llXKN6NGjWLo\n0KFkZmYecrxChQokJSXRv3//kJJJkiRJKq6WLQu2+ps+HcqWhX79oH9/qFXr0OtKR6MQPUJhlZsb\nnJckSZIUipiwA6h4mDRpEgMHDqRRo0ZMmzaNjz/+mI8//php06bRqFEjBgwYwKRJk8KOKUmSJKkY\nyM2Fl16C1q3hggvgvffgb3+DL7+ERx89vKgCaBYfD+npeT8wPT04L0mSJCkUkWjUXx/Tz9e4cWMq\nVarE/PnzKV360AV72dnZXH311ezYsYNly5aFlPDEWLp0KU2bNmXJkiU0adIk7DiSJElSsbJvH0ye\nDMnJkJERbPF3zz3QqROU/ol9Q7Zt20bzhATWJiZC/foQExO0Xunp1J0yhYVpacTFxZ2YF5EkSTpB\n/Hmligq3AVS++PTTT3n00UcPK6oASpcuTefOnbn33ntDSCZJkiSpqPv6a3jsseDrm2+gY0d46ilo\n0eLIY6j+W1xcHAvT0hiclMSiWbPIjkQoHY3SLD6e4RZVkiRJUqgsq5QvKlasyLp16454fv369VSs\nWPEEJpIkSZJU1K1cGayievZZKFUK+vSBgQOhbt3je15cXBzPpKbmb0hJkiRJP5szq5Qvrr/+ekaP\nHs20adMOOR6NRpk+fTqjR4+mffv2x/zcxYsXc+edd9KwYUNOPvlkatWqRdeuXVm9evVh1+bm5vL4\n44/TuHFjypcvT9WqVWndujXLly8/eM3GjRsZNmwYzZo1o0qVKsTFxdGqVSvmz59/2PPmz59Pnz59\nOOecc4iNjaVu3br07duXLVu2HPN7SJIkSTo60Si88Qa0bQvx8fDKKzBsWDCPavTo4y+qJEmSJBVe\nzqxSvti6dStXXnklGRkZnHbaaZx99tkAfPbZZ2zZsoX69evzzjvvHPPWGp07d2bhwoV06dKF888/\nn82bNzNmzBgyMzP58MMPadiw4cFre/XqxdSpU+nZsyfNmzcnMzOTZcuWkZiYSOvWrQEYM2YM999/\nPx07dqRly5ZkZWUxadIkli5dyvjx4+nVq9fB51144YXs2LGDLl26cPbZZ7N27VrGjBlD+fLlWbZs\nGdWrVz8sr3vASpIkScfnu+9g2jQYORL+9S9o3DiYR3XTTXDSSWGnkyRJKpr8eaWKCssq5Zt9+/Yx\nbtw4Xn75ZdavXw9ArVq1aNeuHf369aNs2bLH/MyFCxdy0UUXHTILa82aNTRq1IjOnTszefJkAGbM\nmEG3bt2YPXs2CQkJR3zeqlWrqFGjBlWqVDl47MCBAzRu3JjMzEw2bNhw8Pj777/PpZdeesj9CxYs\n4IorrmDIkCH85S9/Oez5/stfkiRJOjbffANjx8KYMbBlC7RrF5RUV1559POoJEmSlDd/XqmiwrJK\nRVLTpk2JiYlh8eLFAFxyySVEIhEWLlxIbm4u+/btIzY29qifd88995CcnMzu3bt/8r6qVavSqlUr\nnn/++cPO+S9/SZIk6eh89hmkpMCECcHWf7fcAoMGwXnnhZ1MkiSp+PDnlSoqnFmlIicajfL1119T\ntWpVAHbt2sXixYu58MILeeCBB6hUqRIVKlSgbt26eRZKedmyZQuxsbGUL1/+R6/LzMxk9+7dB7+3\nJEmSpKMXjcK770JCQlBKzZwJ/+//wYYN8MQTFlWSJElSSVX6py+RDteqVSsikQivv/46pUuXPvj5\nSKLRKJFIhLfeeutnf+8pU6awadMmkpKSAFi7di3RaJTp06dTpkwZHn30USpWrEhqairdunWjYsWK\nXHPNNUd83po1a5g1axZdu3b90XcASElJISsri65du/7s95AkSZJKiqwseOEFGDECliyBBg3gySch\nMRGOY7dwSZIkScWMZZWOy3/vHhmNRg87VhAyMjL4/e9/T4sWLejZsycQrHYC+Pbbb/nwww+56KKL\nALjhhhuoU6cOSUlJRyyr9u7dS5cuXYiNjeXhhx/+0e/93nvvMWzYMLp27cqVV16Zfy8lSZIkFVM7\ndkByciaPjsxib+YplK+yhLN+9TwXXb6PG24YStmycWFHlCRJklQIWFbpuLzzzjs/+rkgbNmyhXbt\n2nHKKafwwgsvHFwFVa5cOQDq1KlzsKgCiI2N5frrr2fKlCnk5uYSE3Porpc5OTl069aNjIwMXnnl\nFWrUqHHE752RkUHHjh05//zzeeqpp34y66BBg6hUqdIhx7p370737t2P+n0lSZKkomrdOkhNhaee\nymXP3l/AxRvh1tXsrbeXDbltmJiRwfsJCSxMSyMuzsJKkiQpP0ybNo1p06Ydcmznzp0hpZGOjWWV\nfrZ9+/YxZMgQWrVqRfv27Qvke+zcuZO2bduya9cuFixYcEixdPrppwNQvXr1w+6rVq0aWVlZ7Nmz\nhwoVKhxyrm/fvrz00ktMnTr1R1dKbdy4kTZt2nDKKafw8ssvExsb+5N5k5OTHVgoSZKkEmfhQhg5\nEmbNgsqVoW6DN1jecTM0r/3DRTEx0KABaxMTGZyUxDOpqaHllSRJKk7y+mX5pUuX0rRp05ASSUcv\n5qcvkX5cuXLleOKJJ/j6668L5Pn79++nffv2rFmzhnnz5nHef01dPv3006lRowZfffXVYfdu2rSJ\ncuXKHVZU3XfffUyYMIGUlJQfnT/1zTff0KZNG7KysnjttdfyLMQkSZKkkiwnB2bOhBYtgq9PuHfP\n4wAAIABJREFUPoExY2DjRsiuMBwuqZX3jfXrs2jFihMbVpIkSVKhZFmlfNG0aVNWFMBfNHNycuja\ntSsfffQRzz//PBdffHGe13Xt2pUNGzbw5ptvHjy2fft20tLSuOqqqw659pFHHmHEiBEMGTKE/v37\nH/F779mzh+uuu47Nmzfz8ssvU7du3fx5KUmSJKkY2L0bHnwwk8pVttO5MyxL/4SajYbS4tqBdO68\njfLlITsSgf9s332YmJjgvCRJkqQSz20AlS+Sk5O57rrraNiwIb1796Z06fz5R+uee+5h7ty5tG/f\nnu3bt/Pss88ecr5Hjx4A/OEPf2DGjBnceOON3H333VSsWJGxY8eSk5PDQw89dPD62bNnc//993P2\n2Wdz3nnnHfa8Nm3aUK1aNQASExNZvHgxffr0YeXKlaxcufLgdRUqVCAhISFf3lGSJEkqSr78EkaN\ngieeyGXXrrJw4Sa49Qv2nZfJxtyrDplHVToahWg078IqNzc4L0mSJKnEi0Sj/u1AP1+jRo345ptv\n2LJlC2XLluWMM86gXLlyB89Ho1EikQjLly8/pue2atWK9957j7z+MY1EIuTk5Bz8vG7dOu69917m\nz59PVlYWLVq04OGHHz5kT9Zhw4YxbNgwIpHIYc+MRCK8/fbbXH755QDUqVOHDRs25Pm9a9euzeef\nf37Y8e/3gF2yZIkzqyRJklSsLFkSzKOaMQNiY6Fm3fms6PQVtDzr8ItXrqTXZ58BMOHcc6FBgyNe\n48wqSZKkguPPK1VUuLJK+eLUU0+latWqnHPOOUe8JnIcW3y8/fbbR31tnTp1mDlz5o9e86c//Yk/\n/elPR/W8devWHfX3liRJkoqj3FyYNy8oqd59F+rUgREjoHdvuKTDQ9BiaN431q/PolmzeGf6dBYk\nJLA2MRHq14eYmOCh6enUnTKF4WlpJ/aFJEmSJBVKllXKF++8807YESRJkiTlk717YeJESE6G1auh\neXN44QXo0AFKlQquOZp5VHFxcSxMS2NwUhKLZs0iOxKhdDRKs/h4hqelERcXd+JeSpIkSVKhZVkl\nSZIkSQJg82b4+9/h8cdhxw7o1CkorZo3P/zao51HFRcX51Z/kiRJkn5UTNgBVHzs3LmTv/71r7Rp\n04YLLriARYsWAfDtt98yYsQI1qxZE3JCSZIkSXlZvjzY2q92bUhNhZtvho8++oaTTx/Ab4e25tyr\nr6Zh69b0HjCAbdu2AdAsPh7S0/N+YHp6cF6SJEmSjoIrq5QvvvzySy6//HK+/PJL6tWrR0ZGBpmZ\nmQCccsopjBs3jvXr1zNq1KiQk0qSJEmCYFHUa68F86jeeAPOPBOSkqBvXzhwYCstOnRgbY8ewd5/\nkQjk5rIqI4MFCQksTEtj+NChzqOSJEmSlC8sq5Qv7rvvPjIzM/n444+pXr061apVO3guEonQoUMH\n5s2bF2JCSZIkSQD798OUKUFJtWoVNG0KU6dC585QpkxwTe8BDwZFVYMGP9wYEwMNGrA2MZHBSUk8\nk5rqPCpJkiRJ+cKySvni9ddfZ+DAgTRs2JDt27cfdr5OnTps2LAhhGSSJEmSALZtC2ZR/f3vwZ/b\ntw8+X3bZ4WOnFq1YEayoykv9+iyaNQtwHpUkSZKk/GFZpXyxb9++Q1ZT/bfdu3efwDSSJEmSvpeR\nAcnJMGlSUEr16gUDB8I55xz5nuxI5PAG63sxMcF5SZIkSconMWEHUPFQv3593n333SOeT0tL44IL\nLjiBiSRJkqSSKxqFt9+G668PxknNmQNDh8LGjfDYYz9eVAGUjkaDh+QlNzc4L0mSJEn5xLJK+WLQ\noEE899xz/O1vf2Pnzp0A5OTksHr1anr06MEHH3zAoEGDQk4pSZIkFW8HDsDkydCkCVx1FWzYAM88\nA198AUOGwKmnHt1zmsXHQ3p63ifT04PzkiRJkpRP3AZQ+aJHjx6sX7+eIUOG8MADDwBw7bXXEo1G\nKVWqFH/961/p2LFjyCklSZKk4unf/4YnnoDRo2HTJrj2WnjjDWjd+si7+f2Y4UOHsiAhgbWJicHS\nrJgYyM2F9HTqTpnC8LS0/H8JSZIkSSWWZZV+ln379pGWlsYXX3xBtWrV+Pzzz5k5cyarV68mNzeX\nevXq0alTJ375y1+GHVWSJEkqdtauhZQUGD8esrPh5pth0CBo2PDnPTcuLo6FaWkMTkpi0axZZEci\nlI5GaRYfz/C0NOLi4vLnBSRJkiQJyyr9DFu3bqV58+asW7fu4LHy5csze/Zst/yTJEmSCkg0Ch98\nACNGwIsvBlv73Xsv3HEHVK+ef98nLi6OZ1JT8++BkiRJknQEzqzScfvLX/7C+vXrufvuu5k7dy4p\nKSmULVuW3/3ud2FHkyRJkoqd7GyYMQMuuQQuvRRWrYKxY4O5VMOG5W9RJUmSJEknkiurdNxef/11\nbr75Zh599NGDx6pXr0737t359NNPOffcc0NMJ0mSJBUPu3bB009DaiqsXw9XXQXz5kHbtsEoKUmS\nJEkq6vyrjY7bhg0buOyyyw451rJlSwC+/vrrMCJJkiRJxcaGDcH2fjVrwuDBcPnlsHQpzJ8P7dpZ\nVEmSJEkqPlxZpeP23XffUbZs2UOOff85Ozs7jEiSJElSkbd4MYwcCc8/DxUqBLOo7rwTzjgj7GSS\nJEmSVDAsq/SzrFu3jqVLlx78vGPHDgA+++wzKleufNj1TZo0OWHZJEmSpKIiJwfmzoURI+D99+GX\nv4SUFOjVC04+Oex0kiRJklSwLKv0s/zxj3/kj3/842HH77jjjsOORSIRcnJyTkQsSZIkqUjYswcm\nTAiKqTVr4NJLYdYsuOEGKFUq7HSSJEmSdGJYVum4jR8/PuwIkiRJUpG0aROMGQNjx8LOndC5M0yZ\nAs2ahZ1MkiRJkk48yyodt169eoUdQZIkSSpSPvkkmEc1bRqULQt9+0L//lC7dtjJJEmSJCk8llWS\nJEmSVIByc+HVV4OSav58OOssePhhuPVWqFQp7HSSJEmSFD7LKkmSJEkqAPv2wbPPQnIypKfDRRfB\n9Olw441Q2r+JSZIkSdJB/hVJkiRJkvLR1q3w2GPB1/btkJAA48ZBy5YQiYSdTpIkSZIKH8sqSZIk\nScoHq1YFq6gmT4ZSpaB3bxg4EOrVCzuZJEmSJBVullWSJEmSdJyi0WAO1ciR8MorcNpp8Kc/we9+\nB1WqhJ1OkiRJkooGyypJkiRJOkYHDsC0aUFJtXw5/OpXMHEidOsGJ50UdjpJkiRJKlosqyRJkiTp\nKH37LYwdC2PGwObNcN11wdZ/rVo5j0qSJEmSjpdllSRJkiT9hNWrISUFJkyAnBy45RYYNAjq1w87\nmSRJkiQVfZZVkiRJkpSHaBTefx9GjIA5c6BqVRg8GG6/HapVCzudJEmSJBUfllWSJEmS9H9kZcEL\nLwTzqP75z2D11IgRu1m65s/MeG8ZUxdEKB2N0iw+nuFDhxIXFxd2ZEmSJEkq0iyrJEmSJAnYuROe\nfBJGjYKNG+Hqq+Hll+GCC7ZyaacOrO3RAzpfHwynys1lVUYGCxISWJiWZmElSZIkST9DTNgBJEmS\nJClMX3wRzJ8680x44AG46ipYtgzeeAPatoU//PXBoKhq0CAoqgBiYqBBA9YmJjI4KSnU/JIkSZJU\n1FlWSZIkSSqRPvoIbroJ6taFiRPhrrtg/XqYMAF+9asfrlu0YkWwF2Be6tcPzkuSJEmSjpvbAEqS\nJEkqMXJyIC0NRoyADz6AevVg9Gjo2RNiY/O+JzsS+WFF1X+LiQnOS5IkSZKOm2WVJEmSpGIvMxPG\nj4f/z96dR1dV3f0ff98QlEHAgYuIA2IUJYRKUUKl9XFAUR/BpCIiEouooFZFcMChafv012A1FkKQ\nSVRATMAyRK9UnGhpwRbEOickKjihTEGqgAyS3Pv741QsEpQh5GZ4v9bKWtezz9nnu9dyLcL9sPd3\n1Cj48EP4n/+Bp5+GHj2gXr3vfzYxFoNYrOLAKhoNxiVJkiRJ+8ywSpIkSVKt9emnwc6piRNh48bg\n2L8ZM+D00/d8jtSUFJYWFwc9q76ruJjUlJTKK1iSJEmS6iB7VkmSJEmqdd54AzIyoE0bmDABrrsO\nPvgApk3bu6AKIDszk6S8PCgqgmg0uBiNQlERSfn5ZGdmVv4CJEmSJKkOcWeVJEmSpFohGoW5c4N+\nVH/7G7RuDQ8+CNdcA02b7vu84XCYRZEIw7KyWFJQQFkoRGIsRmpKCtmRCOFwuNLWIEmSJEl1kWGV\nJEmSpBpt82Z44gnIyYF334UuXYKj/n7+c0ispL/xhMNhJufmVs5kkiRJkqSdGFZJkiRJqpFWr4Zx\n44Kf9euDcGrSJOjaNd6VSZIkSZL2hmGVJEmSpBqlsBBGjoT8fKhfH669FgYPhqSkeFcmSZIkSdoX\nhlWSJEmSqr1YDF56KehH9eKLcPTR8Pvfw8CBcNhh8a5OkiRJkrQ/DKskSZIkVVvbtsG0acFOqsJC\n+PGPIS8PeveGgw6Kd3WSJEmSpMpgWCVJkiSp2lm3DiZMgDFjYM0a6NEDHnoIzjoLQqF4VydJkiRJ\nqkyGVZIkSZKqjXffhVGj4PHHg6P/+veHoUPh5JPjXZkkSZIk6UAxrJIkSZIUV7EY/P3vwVF/c+bA\nkUfCvffCDTdA8+bxrk6SJEmSdKAZVkmSJEmKi+3bYcaMIKR6/XVISYFJk6BvX2jQIN7VSZIkSZKq\nimGVJEmSpCr173/DI4/A6NHw2WfQvTu88AKcf779qCRJkiSpLjKskiRJklQlPvgAcnPhsceCXVX9\n+sFttwU7qiRJkiRJdZdhlSRJkqQD6p//DI76e+opOOwwGDoUbroJWraMd2WSJEmSpOrAsEqSJElS\npSsrC8KpkSNh8WJo2xbGjoVf/AIaNYp3dZIkSZKk6sSwSpIkSVKl2bgxOOYvNxc++gjOPhueeQYu\nvhgSEuJdnSRJkiSpOjKskiRJkrTfVqyA0aNh4kTYvBn69IHZs6FTp3hXJkmSJEmq7gyrJEmSJO2z\nf/0rOOpvxgw45BC44Qa45RY45ph4VyZJkiRJqikMqyRJkiTtlWgU5swJQqoFC6BNm+DzNdcEgZUk\nSZIkSXvDsEqSJEnSHvnqK3j8cRg1Ct5/H7p2hVmzID0d6tWLd3WSJEmSpJrKsEqSJEnS91q1CsaM\ngQkT4IsvoFcvmDoVfvKTeFcmSZIkSaoNDKskSZIkVejtt4Pj/aZNg4MPhuuug8GDg2P/JEmSJEmq\nLIZVkiRJknaIxeD554OQat48OOYYuO8+GDgQmjWLd3WSJEmSpNrIsEqSJEkSW7dCXh7k5MDSpXDa\nacGOqssug/r1412dJEmSJKk2M6ySJEmS6rDSUhg3DsaOhXXr4JJLYPx4OPNMCIXiXZ0kSZIkqS4w\nrJIkSZLqoOLiYBfV1KmQkAADBsCtt0LbtrveW1payrCsLJYUFlIWCpEYi5GakkJ2ZibhcLjqi5ck\nSZIk1SqGVZIkSVIdEYvB/PkwYgTMnQstW8JvfgPXXw9HHFHxM2vXrqVrejrLMzIgPT3YbhWNsrSk\nhIVpaSyKRAysJEmSJEn7JSHeBUiSJEk6sL7+OthB9eMfQ7du8OmnMGUKfPQR3Hvv7oMqgLuGDw+C\nquTkb88FTEiA5GSW9+vHsKysqliCJEmSJKkWM6ySJEmSaqn16+EPf4Djj4f+/aFVK3jpJXjzzeC/\nDz74h+dYUlgI7dpVPNiuXTAuSZIkSdJ+8BhASZIkqZZZtgxGjYLJk6G8HK66CoYMgfbt936uslDo\n2x1V35WQEIxLkiRJkrQfDKskSZKkWiAWg3/8I+hHFYkER/vdeSfceCMceeS+z5sYiwWTVxRKRaPB\nuCRJkiRJ+8FjACVJkqQarKwM/vQn6NIFzjwTSkrg4Yfhk0/g//5v/4IqgNSUFCgurniwuDgYlyRJ\nkiRpPxhWSZIkSTXQl18Gu6iSkuCKK6BpU3j2WSgqgoEDoWHDynlPdmYmSXl5wcTRaHAxGoWiIpLy\n88nOzKycF0mSJEmS6iyPAZQkSZJqkI8/htxcePRR2LoV+vaFoUOhY8cD875wOMyiSIRhWVksKSig\nLBQiMRYjNSWF7EiEcDh8YF4sSZIkSaozDKskSZKkGmDJkmAn1ezZwS6qm2+Gm26Co48+8O8Oh8NM\nzs098C+SJEmSJNVJhlWSJElSNVVeDs88E4RU//hHcORfbi5cfTU0bhzv6iRJkiRJqhyGVZIkSVI1\ns2kTTJkCo0bB8uVw5pnw1FPQsyfUqxfv6iRJkiRJqlyGVZIkSVI18dlnMGYMTJgAGzdC794wbRqk\npsa7MkmSJEmSDhzDKkmSJCnO3nwTRo6E6dOhUSMYOBBuuQVat453ZZIkSZIkHXiGVZIkSVIcRKPw\n3HNBP6r584Ng6oEH4LrroGnTeFcnSZIkSVLVMaySJEmSqtCWLfDEE5CTAyUlwRF/f/oTXHopJPrb\nuSRJkiSpDvKvw5IkSVIVWLMGxo0Lfj7/HH7+c3j0UejaFUKheFcnSZIkSVL8GFZJkiRJB1BRUbCL\nKi8v2Dl1zTVw662QlBTvyiRJkiRJqh4MqyRJkqRKFovBvHkwciQ8/zy0agW/+x0MGgSHHbbzvaWl\npQzLymJJYSFloRCJsRipKSlkZ2YSDofjswBJkiRJkqqQYZUkSZJUSbZtg+nTg5DqnXegY8egP9Xl\nl8NBB+16/9q1a+mans7yjAxITw/OA4xGWVpSwsK0NBZFIgZWkiRJkqRaLyHeBUiSJEk13eefw/Dh\ncPzxMGAAtG4Nf/0rvP46ZGRUHFQB3DV8eBBUJSd/27gqIQGSk1nerx/DsrKqbA2SJEmSJMWLYZUk\nSZK0j957D375Szj2WMjKgrQ0KC6GOXPgnHO+zZ92Z0lhIbRrV/Fgu3bBuCRJkiRJtZzHAEqSJEl7\nIRaDBQuCo/7mzIFwGO65B264Ifi8N8pCod0nWgkJwbgkSZIkSbWcYZUkSZK0B7Zvh5kzg5Dqtdeg\nfXt49FG48kpo0GDf5kyMxYL0q6JQKhoNxiVJkiRJquU8BlCSJEn6Hl98AQ8+CCecAP36weGHw/PP\nwzvvwDXX7HtQBZCakhKcG1iR4uJgXJIkSZKkWs6wSpIkSarAhx/CkCFBP6pf/QrOOw/efhtefBEu\nuOCH+1HtiezMTJLy8qCoCKLR4GI0CkVFJOXnk52Zuf8vkSRJkiSpmvMYQEmSJOm/LF4MI0ZAQQEc\nemgQWP3yl3DUUZX/rnA4zKJIhGFZWSwpKKAsFCIxFiM1JYXsSITw3jbBkiRJkiSpBjKskiRJUp1X\nXg5PPx2EVIsWQdu2MHYs/OIX0KjRgX13OBxmcm7ugX2JJEmSJEnVmGGVJEmS6qyNG2HyZBg1Kjj2\n76yz4Jln4OKLIcEDsyVJkiRJqhL+FVySJEl1zqefwl13wTHHRBkytJzPN8/juM43UlqvGwXzbuXz\nz0vjXaIkSZIkSXWGO6skSZJUZ7z+enDU34wZ0KhRlIRDphEbFmVD12PZEOoD0ShLS0pYmJbGIntG\nSZIkSZJUJdxZJUmSpFotGoU5c+Dss+G004KeVCNGQM8r7+aLX22Anx4HoVBwc0ICJCezvF8/hmVl\nxbVuSZIkSZLqCsMqSZIk1UqbN8P48XDKKXDJJfD11zBrFrz/PgweDG+89xq0a1fxw+3asaSwsGoL\nliRJkiSpjjKskiRJUq2yejVkZsKxx8LNN8fYHnuD40+7hc8bncdvxnXjuttupbS0lLJQ6NsdVd+V\nkBCMS5IkSZKkA86eVZIkSaoV3nkHRo6EadPgoIPgyis38/yrV/HRdd2g3aVBMPVfPanq1a8PsVjF\ngVU0SmIsVvWLkCRJkiSpDnJnlaq1V199lZtvvpn27dtzyCGH0Lp1a/r06cP777+/y73RaJTx48fT\nsWNHGjVqRPPmzenWrRtvv/32jntWrFjB7373O1JTUzn88MMJh8Occ845/OUvf6nw/V988QWDBg0i\nHA5zyCGHcO655/LGG28csPVKkqS9E4vBCy9A9+7wox/BvHkwfDisWAFfN7iHT67rBsnJFfakin79\nNRQXVzxxcTGpKSlVtxBJkiRJkuowwypVaw888ABPPfUU559/PqNHj2bQoEEsWLCATp06UVRUtNO9\n11xzDbfeeiudO3dmzJgx/OY3v6F169aUlpbuuCcSiZCdnU3btm0ZPnw4v/71r9m4cSPnn38+U6ZM\n2Wm+aDTKxRdfzPTp0xk8eDDZ2dmsXbuWs88+m2XLllXF8iVJ0m5s3QqTJkGHDnDhhbB+fbCj6oMP\n4I474NBDCXpOfU9PqoTERJLy8qCoCKLR4Ho0CkVFJOXnk52ZWXULkiRJkiSpDvMYQFVrt99+O507\ndyYx8dv/Vfv06UOHDh24//77eeKJJwCYMWMGU6dO5amnniItLW2385177rmsWLGCww8/fMe1G264\ngY4dO/Kb3/yGq6++esf1WbNmsWjRImbNmsWll14KwOWXX07btm357W9/S35+fiWvVpIk/ZDSUpgw\nAcaMCT737AnjxsGZZ+56mt8P9aTi4INZNH06w7KyWFJQQFkoRGIsRmpKCtmRCOFw+MAvSJIkSZIk\nGVapejvjjDN2uXbiiSeSnJxMSUnJjmsjR46kS5cupKWlEY1G2bJlC40bN97l2eTk5F2uHXTQQVx0\n0UXk5OTw1Vdf7Xhu1qxZtGzZckdQBdC8eXMuv/xy8vLy2L59O/Xr16+MZUqSpB9QUgI5OTB1apA/\nXX01DBkCbdvu/pnEWOwHe1KFw2Em5+YesLolSZIkSdIP8xhA1TixWIw1a9bQvHlzADZs2MCrr77K\n6aefzr333kuzZs1o0qQJSUlJzJw5c4/mXL16NY0bN6ZRo0Y7rr3xxht06tRpl3s7d+7M5s2bee+9\n9ypnQZIkqUKxGMyfH+yeatcOnnkGMjODflTjxn1/UAUEPafsSSVJkiRJUrVnWKUaJz8/n5UrV9Kn\nTx8Ali9fTiwW48knn2TKlCn88Y9/JD8/n3A4zBVXXMELL7zwvfMtW7aMgoICevXqRei//uX1qlWr\nOOqoo3a5/5trK1eurMRVSZKkb3z9NeTlwWmnwbnnwscfw+TJ8NFH8KtfwRFH7Nk82ZmZ9qSSJEmS\nJKkG8BhA1SglJSXcdNNNdO3alf79+wOwadMmANavX8/ixYvp3LkzAJdccglt2rQhKyuLCy64oML5\nNm/eTO/evWncuDH333//TmNbt27l4IMP3uWZBg0aALBly5ZKW5ckSYJ//xsmToTRo2HlSrjwQnjp\nJejWbfetp75POBxmUSRiTypJkiRJkqo5wyrVGKtXr+biiy/msMMOY9asWTt2QTVs2BCANm3a7Aiq\nABo3bkyPHj3Iz88nGo2SkLDzRsLy8nKuuOIKSkpKeO6552jZsuVO4w0bNmTbtm271LF169ad3itJ\nkvbP8uWQmwuTJsH27XDVVTB0KLRvv/9z25NKkiRJkqTqz7BKNcKXX37JRRddxIYNG1i4cOFOwVKr\nVq0AOPLII3d5rkWLFmzfvp2vvvqKJk2a7DQ2cOBAnn32WaZNm8bZZ5+9y7NHHXVUhUf9rVq1aqf3\nVmTo0KE0a9Zsp2t9+/alb9++u1+kJEl1SCwG//wnjBgBTz8dHO13++3wy19CBX+kS5IkSZJ+wPTp\n05k+ffpO17788ss4VSPtHcMqVXtbt26lZ8+eLFu2jHnz5nHKKafsNN6qVStatmzJZ599tsuzK1eu\npGHDhrsEVXfeeSdTpkwhNzd3R++r7+rYsSMLFy4kFovt1MvqlVdeoXHjxrT9nq7uOTk5dOrUaW+W\nKUlSnVBWBgUFMHIkvPIKnHwyTJgQ7KZy07IkSZIk7buK/rH866+/zmmnnRaniqQ9l/DDt0jxU15e\nTp8+fXjllVeYOXMmXbp0qfC+Pn368MknnzBv3rwd19atW0ckEuHcc8/d6d4HH3yQESNG8Ktf/Ypb\nbrllt+++7LLLWLNmDQUFBTvNOXPmTHr27En9+vX3c3WSJNUdGzZATg6ceCL06QONG8Of/wxLl8Kg\nQQZVkiRJkiTVZe6sUrV2++23M2fOHHr27Mm6devIy8vbaTwjIwOAe+65hxkzZtCrVy9uu+02mjZt\nyoQJEygvL+e+++7bcf9TTz3FXXfdxUknncQpp5yyy3zdu3enRYsWQBBW/eQnP2HAgAEsXbqUI444\ngnHjxhGLxfjd7353gFcuSVLt8MknMHo0PPIIbN4MffsG/ah+/ON4VyZJkiRJkqoLwypVa2+99Rah\nUIg5c+YwZ86cncZCodCOsKpFixa8/PLL3HHHHeTk5LB9+3a6du3KtGnT6NChw45n3n77bQCWLVvG\nVVddtct88+fP3xFWJSQkMHfuXO68805Gjx7Nli1bSE1NZerUqZx00kkHctmSJNV4r74aHPU3cyY0\naRL0orr5Zjj66HhXJkmSJEmSqptQLBaLxbsIqbb45gzY1157zZ5VkqQ6p7wc5swJQqqFC+GEE4Jd\nVFdfDYccEu/qJEmSJKnu8ftK1RTurJIkSdJ++eormDIFRo2CZcvgZz+DggK45BKoVy/e1UmSJEmS\npOrOsEqSJEn7ZOVKGDMGJkyAL7+Eyy6D/HxITY13ZZIkSZIkqSYxrJIkSdJeeeut4Ki/6dOhQQMY\nOBBuuQWOPz7elUmSJEmSpJrIsEqSJEk/KBqF558PQqq//AWOOw7uvx+uvRaaNYt3dZIkSZIkqSYz\nrJIkSdJubdkCeXmQkwPFxdC5Mzz5JPTqBYn+JilJkiRJkiqBXzFIkiRpF2vXwrhxwc+6dZCWBhMn\nwk9/CqFQvKuTJEmSJEm1iWGVJEmSdli6NNhF9cQTUK8eDBgAQ4bAiSfGuzJJkiRJklRbGVZJkiTV\ncbFY0Idq5Eh47jk46ij47W/h+uvh8MPjXZ0kSZIkSartDKskSZLqqK+/hunTg5Dq7bcETm/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"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#code below is to display image in IPython\n",
"from IPython.display import Image\n",
"Image(filename='figure_1.2.png')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looks like it's fits pretty good. Let's check polinomial regression with second and third degree."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"#linear polinom\n",
"regression1 = np.polyfit(x, y, 1)\n",
"y1 = regression1[0]*x+regression1[1]\n",
"#sqare polinom\n",
"regression2 = np.polyfit(x, y, 2)\n",
"y2 = regression2[0]*(x**2)+regression2[1]*x+regression2[2]\n",
"#polinom with degree 3\n",
"regression3 = np.polyfit(x, y, 3)\n",
"y3 = regression3[0]*(x**3)+regression3[1]*(x**2)+regression3[2]*x+regression3[3]\n",
"\n",
"#And plot it\n",
"subplot(311)\n",
"plot(x,y,'co')\n",
"plot(x,y1)\n",
"ylabel('Period')\n",
"title('Linear ')\n",
"subplot(312)\n",
"plot(x,y,'co')\n",
"plot(x,y2)\n",
"ylabel('Period')\n",
"title('Square ')\n",
"subplot(313)\n",
"plot(x,y,'co')\n",
"plot(x,y3)\n",
"xlabel('Temperature')\n",
"ylabel('Period')\n",
"title('Cubic ')\n",
"show() \n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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jzcv0HT4sHT0qlZfb2gYE2CqiDuT8n07/qq/UpkwKLJdanpdcbW2b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\nREREREREREREROTKpbBKpAaSkpJ45JFH6NKlC02bNqVdu3bExsayd+/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ydPavr06YqKilJubq5effVVBQYGavfu3erWrVu98bIGLAAAANAy1e4HVVP5VNfXX2v2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\n1727K3y6/Xb36qgeP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"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#code below is to display image in IPython\n",
"from IPython.display import Image\n",
"Image(filename='figure_1.3.png')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So when you look at these plots it's hard to decide which one is better describe experimental data. So in order to choose which function is better let's use Relative Mean Squared Error parameter.\n",
"Relative Mean squared error as part of sklearn.metrics looks like this:\n",
"rms = sqrt(mean_squared_error(y_expiremental, y_calculated))\n",
"\n",
"So my code will be looks like this:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"#linear polinom\n",
"regression1 = np.polyfit(x, y, 1)\n",
"y1 = regression1[0]*x+regression1[1]\n",
"#sqared error\n",
"rms1 = sqrt(mean_squared_error(y, y1))\n",
"#sqare polinom\n",
"regression2 = np.polyfit(x, y, 2)\n",
"y2 = regression2[0]*(x**2)+regression2[1]*x+regression2[2]\n",
"#sqared error\n",
"rms2 = sqrt(mean_squared_error(y, y2))\n",
"#polinom with degree 3\n",
"regression3 = np.polyfit(x, y, 3)\n",
"y3 = regression3[0]*(x**3)+regression3[1]*(x**2)+regression3[2]*x+regression3[3]\n",
"#sqared error\n",
"rms3 = sqrt(mean_squared_error(y, y3))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And then plot everything) And display error value in Plot title."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"subplot(311)\n",
"plot(x,y,'co')\n",
"plot(x,y1)\n",
"ylabel('Period')\n",
"title('Linear polinom. '+'Mean squared error is '+str(rms1))\n",
"subplot(312)\n",
"plot(x,y,'co')\n",
"plot(x,y2)\n",
"ylabel('Period')\n",
"title('Square polinom.'+'Mean squared error is '+str(rms2))\n",
"subplot(313)\n",
"plot(x,y,'co')\n",
"plot(x,y3)\n",
"xlabel('Temperature')\n",
"ylabel('Period')\n",
"title('Cubic polinom.'+'Mean squared error is '+str(rms3))\n",
"show() \n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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1UGWViIiIiIiIiEgDnDljhk71VUedPOkcGxAA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\nF1+sHb9x40YWLFhAv379GDBggNv9xo0bR1BQEABJSUns2LGD2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WWl2zwqKipcnisiIiIN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\ndHQ04uPjlZb40dHRwbh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"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#code below is to display image in IPython\n",
"from IPython.display import Image\n",
"Image(filename='figure_1.4.png')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So looks like cubic polinom is the best to decribe me expiremental data.\n",
"But in future is better to write a function that can choose automaticaly whats degree is better to use in equations so relative mean square error will have lowest value."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.10"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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